Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (density of states) landscape as a function of training loss and test accuracy.

We explore the possibility of exact algorithmic learning with gradient-based methods and introduce a differentiable framework capable of strong length generalization on arithmetic tasks. Our approach centers on Differentiable Finite-State Transducers (DFSTs), a Turing-complete model family that avoids the pitfalls of prior architectures by enabling constant-precision, constant-time generation, and end-to-end log-parallel differentiable training. Leveraging policy-trajectory observations from expert agents, we train DFSTs to perform binary and decimal addition and multiplication. Remarkably, models trained on tiny datasets generalize without error to inputs thousands of times longer than the training examples. These results show that training differentiable agents on structured intermediate supervision could pave the way towards exact gradient-based learning of algorithmic skills. Code available at \href{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}.

Optimizing training performance in large language models (LLMs) remains an essential challenge, particularly in improving model performance while maintaining computational costs. This work challenges the conventional approach of training LLMs using next-token prediction (NTP), arguing that by predicting information-rich tokens during training, there is a more effective way to train LLMs. We investigate the impact of the proposed solution in three kinds of tasks for LLMs: arithmetic, multi-label classification of text, and natural-language generation. This work offers a principled approach to optimizing LLM training, advancing both model performance and theoretical understanding of the target-token selection strategies.

Pretrained language models (LMs) are prone to arithmetic errors. Existing work showed limited success in probing numeric values from models' representations, indicating that these errors can be attributed to the inherent unreliability of distributionally learned embeddings in representing exact quantities. However, we observe that previous probing methods are inadequate for the emergent structure of learned number embeddings with sinusoidal patterns. In response, we propose a novel probing technique that decodes numeric values from input embeddings with near-perfect accuracy across a range of open-source LMs. This proves that after the sole pre-training, LMs represent numbers with remarkable precision. Finally, we find that the embeddings' precision, judged by our probe's accuracy, explains a large portion of LM's errors in elementary arithmetic, and show that aligning the embeddings with the pattern our probes discover can mitigate these errors.

We introduce the Neural Power Unit (NPU).

This study explores the intersection of electroencephalography (EEG) microstates and Large Language Models (LLMs) to enhance the assessment of cognitive load states. By utilizing EEG microstate features, the research aims to fine-tune LLMs for improved predictions of distinct cognitive states, specifically 'Rest' and 'Load'. The experimental design is delineated in four comprehensive stages: dataset collection and preprocessing, microstate segmentation and EEG backfitting, feature extraction paired with prompt engineering, and meticulous LLM model selection and refinement. Employing a supervised learning paradigm, the LLM is trained to identify cognitive load states based on EEG microstate features integrated into prompts, producing accurate discrimination of cognitive load. A curated dataset, linking EEG features to specified cognitive load conditions, underpins the experimental framework. The results indicate a significant improvement in model performance following the proposed fine-tuning, showcasing the potential of EEG-informed LLMs in cognitive neuroscience and cognitive AI applications. This approach not only contributes to the understanding of brain dynamics but also paves the way for advancements in machine learning techniques applicable to cognitive load and cognitive AI research.

While recent work has begun to uncover the internal strategies that Large Language Models (LLMs) employ for simple arithmetic tasks, a unified understanding of their underlying mechanisms is still lacking. We extend recent findings showing that LLMs represent numbers in a digit-wise manner and present evidence for the existence of digit-position-specific circuits that LLMs use to perform simple arithmetic tasks, i.e. modular subgroups of MLP neurons that operate independently on different digit positions (units, tens, hundreds). Notably, such circuits exist independently of model size and of tokenization strategy, i.e. both for models that encode longer numbers digit-by-digit and as one token. Using Feature Importance and Causal Interventions, we identify and validate the digit-position-specific circuits, revealing a compositional and interpretable structure underlying the solving of arithmetic problems in LLMs. Our interventions selectively alter the model's prediction at targeted digit positions, demonstrating the causal role of digit-position circuits in solving arithmetic tasks.

Electroencephalogram (EEG) data is crucial for diagnosing mental health conditions but is costly and time-consuming to collect at scale. Synthetic data generation offers a promising solution to augment datasets for machine learning applications. However, generating high-quality synthetic EEG that preserves emotional and mental health signals remains challenging. This study proposes a method combining correlation analysis and random sampling to generate realistic synthetic EEG data. We first analyze interdependencies between EEG frequency bands using correlation analysis. Guided by this structure, we generate synthetic samples via random sampling. Samples with high correlation to real data are retained and evaluated through distribution analysis and classification tasks. A Random Forest model trained to distinguish synthetic from real EEG performs at chance level, indicating high fidelity. The generated synthetic data closely match the statistical and structural properties of the original EEG, with similar correlation coefficients and no significant differences in PERMANOVA tests. This method provides a scalable, privacy-preserving approach for augmenting EEG datasets, enabling more efficient model training in mental health research.

The chain of thought is fundamental in Transformers, which is to perform step-by-step reasoning. Besides what intermediate steps work, the order of these steps critically affects the difficulty of the reasoning. This study addresses a novel task of unraveling chain of thought - reordering decoder input tokens to a learning-friendly sequence for Transformers to learn arithmetic tasks. The proposed pipeline first trains a Transformer on a mixture of target sequences arranged in different orders and then identifies benign orders as those with fast loss drops in the early stage. As the search space grows factorially with sequence length, we propose a two-stage hierarchical approach for inter- and intra-block reordering. Experiments on four order-sensitive arithmetic tasks show that our method identifies a learning-friendly order out of a few billion candidates. Notably, on the multiplication task, it recovered the reverse-digit order reported in prior studies.